I have a special request from a customer regarding an eCommerce website project and I'm checking if all requirements are possible thanks to open cart. The 2 specific features are :

1) birth list : idea is to have a module who allow customer to create their own birth list with website products of course and manage it : add/remove producst, share list with friends etc.... . Is it possible with opencart? Or possibility to develop it?

2) stock synchronisation : the main products stock in website but there is also a physical shop. when a sale is done from the physical shop, on-mine sotck (website) have to be updated. Is it possible with opencart? Or possibility to develop it?

Also, all the sales, add to cart etc...have to be tracked and followed throught Google Analytics.
Does opencart can work with transactionnal Google Analytics ?

1) birth list : idea is to have a module who allow customer to create their own birth list with website products of course and manage it : add/remove producst, share list with friends etc.... . Is it possible with opencart? Or possibility to develop it?

This does not exist by default, the OC Wishlist could eventually be modified, to make such work.
But most everything is possible, it only depends on your budget.

2) stock synchronisation : the main products stock in website but there is also a physical shop. when a sale is done from the physical shop, on-mine sotck (website) have to be updated. Is it possible with opencart? Or possibility to develop it?

Also, all the sales, add to cart etc...have to be tracked and followed throught Google Analytics.
Does opencart can work with transactionnal Google Analytics ?

Just check with Google and in the OC Extension Section for such Mods, and it also depends on the
OC Version used. BTW, latest versions usually have a lower amount of available Extensions.
Good Luck !
Ernie
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1) but from your point of view, how much will it cost to develop/implement this kind of feature?
Well, how much is the price a new Automobile ? It all depends on the features, one requires, it
might be between 25 and 100 US$ for such a Mod, I assume. But I don't do such work, so I cannot tell.
---2) but POS is to generate orders from pysical store to open cart no? what I need is only to synchronise stock.
In that pysical store, I assume, they have a cash register, or even some PC Software, to create receipts, and/or
save the transactions in some ways. But instead of using this, POS can be used, to exactly do the this Job, but
with/on the Opencart Site. It's works this way in all warehouses and larger stores everywhere.
Ernie